Quantum field theory

Fields of reality

When one wants to talk about the matter and its behavior in the world of the infinitely small particles, it addresses the quantum field theory.Quantum field theory allows, understand particle physics where in some situations, the number of incoming particles in a portion of space, fluctuates and varies outgoing number. The number of particles changed when, for example, 1 atom in an initial condition matched 1 atom plus one photon in a final state. In other words, a photon is suddenly pulled out of the vacuum and appeared in the electromagnetic field.Quantum theory tells us that in the real world, everything is "field".We bathe completely, to the depths of ourselves, in fields, multiple, diverse, with amazing features.The field is a fundamental concept in physics, it is made up of nothing else, it is itself which is the real world, the fields carry the energy of all that exists in the universe, atoms to large galactic structures.Magnetism, gravity, nuclear force light and other physical phenomena are carried by fields.The most surprising is that the matter itself, the one we made, consists of a set of fields, electrons and protons, are themselves fields, and we are made up of fields escaping intuition. In other words, we are made of an aggregate of quantum particles bathed in ghostly fields that carry the energy of the particles throughout the space around them.With the concept of field, the vision of the nature of things is overwhelming, the reality becomes strange and escapes our 5 senses. The reality is not simply explained by the presence of matter, but also by the exchange and interaction between real objects and virtual objects of low energy quantum fields.

In the quantum world all particles of the standard model, fermions and bosons emerge vibrations in a field. This is also the basic concept of the operation of particle accelerators like the Large Hadron Collider, the LHC.When scientists want to see a particle, they cause collisions whose energy corresponds to the particle in question.Quarks and electrons constitute ordinary matter, or the matter above absolute zero (-273.15 ° C) emits radiation, ie light that moves in a field. Each type of fermion and every type of Boston has its own field, the particles are regarded as excited states of these fields. The wave-particle duality of light, has been extended to electrons in 1929 by the French mathematician and physicist Louis de Broglie (1892 − 1987), then all particles.However, our mind needs image of our world, to feed its intuition and visualize the concepts, but conceptualize quantum and all quantum fields in which we exist is not easy. Everything is "field" but quantum fields that are bubbling and loaded dynamic systems, are all subsets of the gravitational field or the electromagnetic field, the only two fundamental fields of nature.

nota : pre-Socratic as Leucippus (5th century BC.) and his disciple Democritus (460 -. 370 BC), thought that the real was made of atoms and vacuum. "He (Leucippe) believed that all things are unlimited and mutually transform into each other, and that the universe is both empty and full of body. "(Diogenes Laertius poet and biographer of the 3rd century AD).

Image : representation of the molecular wave function showing the border of the atoms in a molecule. Which begins and ends an atom? The atom is a field and it is the field lines which define its volume. No one has seen the fields of quantum physics, but it could look like this computer-generated image. When atoms bind them, their fields are deformed, this deformation is that characterizes bonds. The particles of the quantum theory are not "balls", but undulations, fields which have a wavelength, this wavelength is the size of the particle, and the field energy of the particle. credit image : T.A. Keith.

What is a field?

In physics, a field that is three things connected in a system with a large number of objects. The first is a portion of space delimited, the second is a measurable physical quantity, and the third is a relationship between the portion of space in the physical quantity.In other words, a field is filled with physical quantities measurable, quantifiable objects using an instrument, where each point of the space portion is linked to the physical quantity by a match, or a function.For example (see image) atmospheric pressure, air temperature, wind speed but also the rain, magnetism, gravity, radioactivity, can be represented by fields.The fields are scalar or vector.A scalar field is measurable by a simple grandeur for example, temperature or mass defined measurable physical quantity entirely by a single value.A vector field is associated with a vector quantity, ie, a quantity of which only one value is not sufficient, you have more direction ie a direction and line as in a velocity field wind.How to represent a field?For a scalar field simply represent the areas where the value is the same as in a field of temperatures or pressures (1st and 3rd thumbnail).For a vector field simply represent the field lines where each point is a tangent vector field, as in the field of wind direction or in a magnetic field (2nd and 4th thumbnail). The energy of the field, fades into space, this is the reason why outside the electromagnetic field generated by a broadcasting station, it no longer captures all emissions and when we brutally interrupted an electromagnetic field, there is a spark, it shows that the field contains an energy well.And the quantum field?In quantum physics, it is not use the concept of corpuscle since quantum particles do not corpuscles but mathematical quantities represented by state vectors in the Hilbert space. This concept escapes intuition. As the vision is the most powerful sense of our senses, it is natural to search for images that facilitate the understanding of the quantum field.

The quantum field fills all space, it is a vector field of subatomic particle whose size is quantified (taken in a finite set of values) and the relationship is a wave function (state vector), it which allows to know all the information of the system and gives every particle typical interference properties of a wave.In the quantum world all particles in the ground state (unexcited) are waves. If we look at a hadron field very closely, we see virtual particles, partons (gluons and quarks) that move, appearing and disappearing in the empty space.If we look at a field carried by the weak nuclear force, we see W and Z bosons If we look at an electromagnetic field, we see photons, and if we could watch a gravitational field we would see gravitons, but gravity is a very low force, and the rare gravitons are difficult to see.Thus, the virtual and real particles of matter bathe in these bubbling fields, occasionally transferring their energy. This is what scientists cause in a collider. In a collider, when an electron and positron meet, they annihilate and transfer their energy to the vacuum tingling, this energy creates real material particles that come out of the vacuum and appear a few "moments" on computer screens .A field is a bubbling system, a ripple, vibration, oscillation, a wave which has a wavelength and hence frequency, and thanks to the ingenious formula e = hv Max Planck (1858 - 1947), a field has also energy (e is the energy of something moving, h is Planck's constant and ν, the Greek letter nu, frequency). This torque, energy and frequency, characterized the field at each point in space. Each point in space allows the emergence or annihilation of particles.

nota : when we want to emphasize an idea, an intuition of a fundamental or profound concept, one is confronted with a problem of translation.
How, precisely, in the language of every day, something exact, while giving good intuition but false, of what we want to talk?
It is useless to say the exact things if no one understands the scientific formalism.
Give a good intuition about something unintuitive is extremely delicate.

Image : A field can not be represented by an image, however, can be mapped on.

Video : The nucleon field. No optical device allows us to see the bustle of small particles inside a proton or a neutron, but the image layout, same false, is fundamental to understanding the concepts. So in this video, a simulation of the mathematical concept of the nucleon was conducted to allow us to make an intuition of what happens inside protons and neutrons. Credit : 1996 - Jean-François Colonna (Centre de Mathématiques appliquées de l'Ecole Polytechnique et France Télécom).

The wave function is one of the fundamental concepts of quantum mechanics.
It corresponds to the representation of the quantum state of a system in an infinite-dimensional basis.
The wave function gives every particle, typical interference properties of a wave.
In classical mechanics we represent the movement by particles which move in space, in quantum mechanics we represent the real and imaginary particles by wavefunctions.
These wave functions corresponding to stationary or non-stationary states (time-dependent) of energy.
In the standard model of particle physics, a hadron is composed of quarks and/or anti-quarks and gluons.
Subatomic particles constituting a hadron are called partons.
Quarks or antiquarks present in the hadron are called valence quarks while the quark-antiquark pairs and gluons that appear and disappear permanently in the hadron, are called virtual particles.
Gluons are the vectors of the strong force that holds quarks together.
Bosons are subatomic particles that transmit information different forces or interactions. Bosons are social particles, they like to mix, like light which mixes with the light, the photons are bosons.
The photon is the particle mediator the electromagnetic interaction.
The gluon is the messenger of the strong nuclear force, it confines quarks binding together very strongly.
Bosons Z 0 and W ± are the gauge bosons of the weak interaction.
The two categories of the nature of the particles are fermions and bosons.
In particle physics, the model of partons was proposed by Richard Feynman in 1969 to describe the structure of hadrons (protons, neutrons) and model the interactions with hadrons of high energy.
Partons are quarks, antiquarks and gluons that make up hadrons.
Quarks present in the hadron throughout its existence are called valence quarks, the opposite of virtual particles (quark-antiquark pairs and gluons) that appear and disappear permanently in the hadron. Gluons are the
vectors of the strong force that holds quarks together.
A hadron is a compound of partons, subatomic particles governed by the strong interaction.
Fermions are subatomic particles (electrons, neutrinos and quarks) of the matter.
All matter that makes up the objects around us are made of fermions. Fermions are asocial particles, in other words they refuse to reduce their living space, this is why the matter is not compressible and that we can walk on the floor.
The two categories of nature particles are fermions and bosons.
The Hilbert space, David Hilbert (1862 - 1943), is a vector space equipped with a scalar product for measuring lengths and angles.
Hilbert space generalizes the notion of classical Euclidean space (two-dimensional plane and three-dimensional space) to spaces of any dimension, finite or infinite.
The Hilbert space is an abstract mathematical concept which allows to apply the techniques of mathematical analysis to all spaces.
These techniques are used in theories of equations partial derivative, in quantum mechanics, Fourier analysis, thermodynamics.